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Multistable and excitable behavior in semiconductor ring lasers with broken Z2-symmetry

Abstract

We study the bifurcation scenario and the evolution of the counter-propagating modes in a semiconductor ring laser when their symmetry is broken. We show how a two-dimensional asymptotic model for this asymmetric ring laser can be used to interpret and predict regions of multistability and excitability in the laser. The theoretical predictions and insights in these different dynamical regimes of the asymmetric semiconductor ring laser are confirmed and further explored experimentally in a semiconductor ring laser set-up that allows to controllably break the Z2-symmetry of the laser.

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References

  • L.N. Menegozzi, W.E. Lamb, Phys. Rev. A 8, 2103 (1973)

    Google Scholar 

  • H. Zeghlache, P. Mandel, N.B. Abraham, L.M. Hoffer, G.L. Lippi, T. Mello, Phys. Rev. A 37, 470 (1988)

    Google Scholar 

  • M. Sargent III, Phys. Rev. A 48, 717 (1993)

  • C. Etrich, P. Mandel, N.B. Abraham, H. Zeghlache, IEEE J. Quantum Electron. 28, 811 (1992)

    Google Scholar 

  • M.T. Hill, H.J.S. Dorren, T. de Vries, X.J.M. Leijtens, J.H. den Besten, B. Smalbrugge, Y.S. Oei, H. Binsma, G.D. Khoe, M.K. Smit, Nature 432, 206 (2004)

  • K.A. Wiesenfeld, E. Knobloch, Phys. Rev. A 26, 2946 (1982)

    Google Scholar 

  • K.R. SchenkHoppe, Nonlinear Dynamics 11, 255 (1996)

    Google Scholar 

  • Y. Kuznetsov, Elements of Applied Bifurcation Theory, 3rd edition (Springer, New York, 2004)

  • J. Guckenheimer, P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer-Verlag, New York, 2002)

  • J.H.P. Dawes, J.R. Gog, J. Math. Biol. 45, 471 (2002)

    Google Scholar 

  • G. Schöner, Biol. Cybern. 63, 257 (1990)

    Google Scholar 

  • E.H. Dowell, AIAA J. 4, 1267 (1966)

    Google Scholar 

  • E. Knobloch, M.R.E. Proctor, J. Fluid Mech. 108, 291 (1981)

    Google Scholar 

  • G. Dangelmayer, E. Knobloch, M. Wegelin, Europhys. Lett. 16, 723 (1991)

  • E. D'Angelo, E. Izaguirre, G. Mindlin, G. Huyet, L. Gil, J.R. Tredicce, Phys. Rev. Lett. 68, 3702 (1992)

    Google Scholar 

  • R. Lopez-Ruiz, G.B. Mindlin, C. Perez-Garcia, J.R. Tredicce, Phys. Rev. A 49, 4916 (1994)

    Google Scholar 

  • P. Holmes, D. Rand, Int. J. Non-Linear Mech. 15, 449 (1980)

  • T. Krauss, P.J.R. Laybourn, J.S. Roberts, Electron. Lett. 26, 2095 (1990)

  • M. Sorel, J.P.R. Laybourn, A. Sciré, S. Balle, G. Giuliani, R. Miglierina, S. Donati, Opt. Lett. 27, 1992 (2002)

    Google Scholar 

  • J.J. Liang, S.T. Lau, M.H. Leary, J.M. Ballantyne, Appl. Phys. Lett. 70, 1192 (1997)

    Google Scholar 

  • V.R. Almeida, M. Lipson, Opt. Lett. 29, 2387 (2004)

    Google Scholar 

  • B. Li, M.I. Memon, G. Mezosi, G. Yuan, Z. Wang, M. Sorel, S. Yu, IEEE Photon. Technol. Lett. 20, 770 (2008)

    Google Scholar 

  • Z. Wang, G. Yuan, G. Verschaffelt, J. Danckaert, S. Yu, IEEE Photon. Technol. Lett. 20, 1228 (2008)

    Google Scholar 

  • S. Fürst, M. Sorel, IEEE Photon. Technol. Lett. 20, 366 (2008)

    Google Scholar 

  • T. Pérez, A. Sciré, G. Van der Sande, P. Colet, C. Mirasso, Opt. Express 15, 1294112948 (2007)

    Google Scholar 

  • G. Yuan, S. Yu, IEEE J. Quantum Electron. 44, 41 (2008)

    Google Scholar 

  • M. Waldow, T. Plotzing, M. Gottheil, M. Först, J. Bolten, T. Wahlbrink, H. Kurz, Opt. Express 16, 7693 (2008)

    Google Scholar 

  • A.R. Bahrampour, S.S. Zakeri, S.M.A. Mirzaee, Z. Ghaderi, F. Farman, Opt. Commun. 282, 2451 (2009)

  • S.J. Chang, C.Y. Ni, Z.P. Wang, Y.J. Chen, IEEE Photon. Technol. Lett. 20, 1021 (2008)

    Google Scholar 

  • L. Gelens, S. Beri, G. Van der Sande, J. Danckaert, N. Calabretta, H.J.S. Dorren, R. Nötzel, E.A.J.M. Bente, M.K. Smit, Opt. Express 16, 16968 (2008)

    Google Scholar 

  • L. Gelens, G. Van der Sande, S. Beri, J. Danckaert, Phys. Rev. E 79, 016213 (2009)

    Google Scholar 

  • S. Zhang, Y. Liu, D. Lenstra, M.T. Hill, H.Ju, G. Khoe, H.J.S. Dorren, IEEE J. Sel. Top. Quantum Electron. 10, 1093 (2004)

    Google Scholar 

  • V.R. Almeida, C.A. Barrios, R.P. Panepucci, M. Lipson, M.A. Foster, D.G. Ouzounov, A.L. Gaeta, Opt. Lett. 29, 2867 (2004)

    Google Scholar 

  • R. Ciegis, M. Radziunas, M. Lichtner, Math. Modelling Anal. 13, 327 (2009)

    Google Scholar 

  • J. Javaloyes, S. Balle, IEEE J. Quantum Electron. 45, 431 (2009)

    Google Scholar 

  • S. Beri, L. Gelens, M. Mestre, G. Van der Sande, G. Verschaffelt, A. Sciré, G. Mezosi, M. Sorel, J. Danckaert, Phys. Rev. Lett. 101, 093903 (2008)

    Google Scholar 

  • L. Gelens, S. Beri, G. Van der Sande, G. Mezosi, M. Sorel, J. Danckaert, G. Verschaffelt, Phys. Rev. Lett. 102, 193904 (2009)

    Google Scholar 

  • S. Beri, L. Mashall, L. Gelens, G. Van der Sande, G. Mezosi, M. Sorel, J. Danckaert, G. Verschaffelt, Phys. Lett. A 374, 739 (2010)

    Google Scholar 

  • G. Van der Sande, L. Gelens, P. Tassin, A. Sciré, J. Danckaert, J. Phys. B 41, 095402 (2008)

    Google Scholar 

  • J.Y. Lee, X.S. Luo, A.W. Poon, Opt. Express 15, 14650 (2007)

    Google Scholar 

  • C.M. Kim, J. Cho, J. Lee, S. Rim, S.H. Lee, K.R. Oh, J.H. Kim, Appl. Phys. Lett. 92, 131110 (2008)

    Google Scholar 

  • J. Wiersig, S.W. Kim, M. Hentschel, Phys. Rev. A 78, 053809 (2008)

    Google Scholar 

  • L. Shang, L.Y. Liu, L. Xu, Opt. Lett. 33, 1150 (2008)

    Google Scholar 

  • M. Hentschel, T.Y. Kwon, Opt. Lett. 34, 163 (2009)

    Google Scholar 

  • P.A. Khandokhin, I.V. Koryukin, Y.I. Khanin, P. Mandel, IEEE J. Quantum Electron. 31, 647 (1995)

    Google Scholar 

  • E. Doedel, T. Fairgrieve, B. Sandstede, A. Champneys, Y. Kuznetsov, X. Wang, http://indy.cs.concordia.ca/auto/main.html (1997)

  • V.I. Melnikov, Phys. Rep. 209, 1 (1991)

    Google Scholar 

  • M.A. Larotonda, A. Hnilo, J.M. Mendez, A. Yacomotti, Phys. Rev. A 65, 033812 (2002)

    Google Scholar 

  • J.L.A. Dubbeldam, B. Krauskopf, D. Lenstra, Phys. Rev. E 60, 6580 (1999)

  • S. Wieczorek, B. Krauskopf, D. Lenstra, Phys. Rev. Lett. 88, 063901 (2002)

  • H.J. Wünsche, O. Brox, M. Radziunas, F. Henneberger, Phys. Rev. Lett. 88, 023901 (2002)

    Google Scholar 

  • D. Goulding, S.P. Hegarty, O. Rasskazov, S. Melnik, M. Hartnett, G. Greene, J.G. McInerney, D. Rachinskii, G. Huyet, Phys. Rev. Lett. 98, 153903 (2007)

    Google Scholar 

  • E.M. Izhikevich, Int. J. Bifur. Chaos 10, 1171 (2000)

    Google Scholar 

  • A.M. Yacomotti, M.C. Eguia, J. Aliaga, O.E. Martinez, G.B. Mindlin, A. Lipsich, Phys. Rev. Lett. 83, 292 (1999)

  • B. Kelleher et al., Opt. Lett. 34, 440 (2009)

    Google Scholar 

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Gelens, L., Beri, S., Van der Sande, G. et al. Multistable and excitable behavior in semiconductor ring lasers with broken Z2-symmetry. Eur. Phys. J. D 58, 197–207 (2010). https://doi.org/10.1140/epjd/e2010-00042-7

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  • DOI: https://doi.org/10.1140/epjd/e2010-00042-7

Keywords

  • Hopf Bifurcation
  • Bifurcation Diagram
  • Stable Manifold
  • Pitchfork Bifurcation
  • Homoclinic Bifurcation